Calculating Time for Sphere Separation in Liquid using Open Integration Method

[chronicals]

Homework Statement

The relative velocity of two small spheres subjected to a constant force in a liquid is given by u = uo/f where f is the drag correction factor and u0 is the relative velocity of the spheres when they are far apart. The drag coefficient factor, f, is a function of (r/a) where a is the radius of each sphere and r is the center-to-center distance. Given the following data for the correction factor estimate the time at which it takes the spheres to travel apart from r=22 μm to r=32 μm when u0=1 mμ/s and a=10 μm
using an appropriate open integration formula. (Hint: dt=dr/u )
r/a: 2.1 2.5 3.0 3.5
f: 4.03 1.72 1.37 1.24

Homework Equations

The Attempt at a Solution

I don't understand the problem, can you explain what i should do firstly?

 

[gabbagabbahey]

Let's imagine for a second, that you were given the exact functional form of f\left(\frac{r}{a}\right)...what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?

 

[chronicals]

Let's imagine for a second, that you were given the exact functional form of f\left(\frac{r}{a}\right)...what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?

Can you give me the function which i should integrate, the problem is very complex and difficult to solve for me

 

[gabbagabbahey]

Again, all I'm asking is that if I gave you f\left(\frac{r}{a}\right)...what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?